Respuesta :
Answer:
A) [tex]25x^2y^{22}[/tex]
Step-by-step explanation:
The given expression is [tex](5xy^{5})^2 . (y^3)^4[/tex]
Here we have to use exponent rules and simplify the expression.
Power rule : [tex](a^m)^n = a^{mn}[/tex]
Using the above rule, we can write
[tex](5xy^{5} )^2 = 5^2.x^2.y^{5*2}[/tex]
= [tex]25.x^2.y^10[/tex]
Again using the power rule
[tex](y^{3} )^4 = y^12[/tex]
Now we have to put together this expression, we get
= [tex]25.x^2.y^{10} .y^{12}[/tex]
Now we have to use product rule.
Product rule: [tex]a^m . a^n = a^{m + n}[/tex]
Using this rule, we can simplify further
= [tex]25..x^2.y^{10 +12}[/tex]
= [tex]25x^2y^{22}[/tex]
